Question

Brenda said that 5/2 divided by 1/4 equals 10. How do yo know without dividing whether Brenda's statement is reasonable? Justify your answer by showing how to find quotient.

Answer 1

I'll just help with proving whether she is correct.

First of all, a fraction divided by a fraction can be made into multiplication since the division of two fractions is kinda difficult

so remember keep, change, flip

keep the first fractions, change the division symbol into multiplication, then flip the fraction i.e. 1/2 becomes 2/1

so 5/2 divided by 1/4 becomes
5/2 * 4/1
which then solved becomes
20/2 which is simplified to 10

Hope this helps :)

Answer 2

Brenda's statement is reasonable.

Explanation:

Brenda said that

`((5)/(2))/((1)/(4))=10`

We need to check whether Brenda's statement is reasonable of not.

Multiply the above equation by 1/4.

`((5)/(2))/((1)/(4))* (1)/(4)=10* (1)/(4)`

`(5)/(2)=(10)/(4)`

`(5)/(2)=(5)/(2)`

`LHS=RHS`

So, Brenda's statement is reasonable.

We need find the quotient of

`((5)/(2))/((1)/(4))`

It can be written as

`(5)/(2)* (4)/(1)}`

`(20)/(2)`

Cancel out the common factors.

`10`